Coordinate geometry - intersection points?

[vzzai]

I know that if 2 equations are given we could find the intersection by solving the equations.
But, what if an intersection point (equation) is given, and asked to find out if this is an intersection of 2 lines?
1) gives one of the equations

Is that enough information to solve?

I'm sorry, if the question sounds vague but I'm curious to know the method.

[neelgandham]

If a*x + b*y = c and a1*x + b1*y = c1 are the equations of the two lines and the intersection point of these lines is (b,d), then the point should satisfy both the line equations. i.e. a*b + b*d should be equal to c and a1*b + b1*d should be equal to c1. Only if both the conditions are satisfied, one can tell that the point is the intersection point !

Hope that answers your question!

[Anurag@Gurome]

I know that if 2 equations are given we could find the intersection by solving the equations.
But, what if an intersection point (equation) is given, and asked to find out if this is an intersection of 2 lines?
1) gives one of the equations

Is that enough information to solve?

I'm sorry, if the question sounds vague but I'm curious to know the method.

What can be understood from your query is that if the equation of one of the lines is given say
ax + by = c, then we need to determine whether(p,q) is a point of intersection of this line and one more line.
Firstly this point (p,q) should lie on the line ax + by = c.
This means that ap + bq = c should be true.
Then, obviously, (p, q) can be the point of intersection of the line ax + by = c and any other line that passes through this point.

[vzzai]

Thank you Anurag. Your explanation clarifies my vague question.

[shekhar.kataria]

I know that if 2 equations are given we could find the intersection by solving the equations.
But, what if an intersection point (equation) is given, and asked to find out if this is an intersection of 2 lines?
1) gives one of the equations

Is that enough information to solve?

I'm sorry, if the question sounds vague but I'm curious to know the method.

What can be understood from your query is that if the equation of one of the lines is given say
ax + by = c, then we need to determine whether(p,q) is a point of intersection of this line and one more line.
Firstly this point (p,q) should lie on the line ax + by = c.
This means that ap + bq = c should be true.
Then, obviously, (p, q) can be the point of intersection of the line ax + by = c and any other line that passes through this point.

HI Anurag

I am little confused between ur explanation and the Question asked.

I understand your explanation above but the Question says that you know the intersection point and the equation of the one line and we need to know whether this point is an intersection point of the two line. Now this may be a interaction point as u proved above but the second line may not pass through this point.

I am not sure may be i am not righly interpretting the Question. Please clerify.

Thanks in advance.